Absence of isolated critical points with nonstandard critical exponents in the four-dimensional regularization of Lovelock gravity

Abstract

Hyperbolic vacuum black holes in Lovelock gravity theories of odd order $N$, in which $N$ denotes the order of higher-curvature corrections, are known to have the so-called isolated critical points with nonstandard critical exponents (as $\alpha =0$, $\beta =1$, $\gamma =N-1$, and $\delta =N$), different from those of mean-field critical exponents (with $\alpha =0$, $\beta =1/2$, $\gamma =1$, and $\delta =3$). Motivated by this important observation, here, we explore the consequences of taking the $D\to 4$ limit of Lovelock gravity and the possibility of finding nonstandard critical exponents associated with isolated critical points in four-dimensions by use of the four-dimensional regularization technique, proposed recently by Glavan and Lin \cite{Glavan2020}. To do so, we first present ${\text{AdS}}_4$ Einstein-Lovelock black holes with fine-tuned Lovelock couplings in the regularized theory, which is needed for our purpose. Next, it is shown that the regularized $4D$ Einstein-Lovelock gravity theories of odd order $N>3$ do not possess any physical isolated critical point, unlike the conventional Lovelock gravity. In fact, the critical (inflection) points of the equation of state always occur for the branch of black holes with negative entropy. The situation is quite different for the case of the regularized $4D$ Einstein-Lovelock gravity with cubic curvature corrections ($N=3$). In this case ($N=3$), although the entropy is non-negative and the equation of state of hyperbolic vacuum black holes has a nonstandard Taylor expansion about its inflection point, but there is no criticality associated with this special point. At the inflection point, the physical properties of the black hole system change drastically ...

arXiv comment11 pages, 4 figures, 1 table, with minor edits (two new paragraphs were added)

References in corpus (54)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• P-V criticality of charged AdS black holes
• Enthalpy and the Mechanics of AdS Black Holes
• GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence
• Black hole chemistry: thermodynamics with Lambda
• Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Pressure and volume in the first law of black hole thermodynamics
• The cosmological constant and the black hole equation of state
• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• Reentrant Phase Transitions in Rotating AdS Black Holes
• Multiple Reentrant Phase Transitions and Triple Points in Lovelock Thermodynamics
• Holographic Heat Engines
• Insight into the Microscopic Structure of an AdS Black Hole from Thermodynamical Phase Transition
• Kerr-AdS analogue of triple point and solid/liquid/gas phase transition
• Smarr Formula and an Extended First Law for Lovelock Gravity
• Horndeski Gravity as $D\to 4$ Limit of Gauss-Bonnet
• Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?
• Joule-Thomson Expansion of Charged AdS Black Holes
• Superfluid Black Holes
• On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions
• The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review
• A consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity
• A note on the novel 4D Einstein-Gauss-Bonnet gravity
• Joule-Thomson Expansion of Kerr-AdS Black Holes
• P-V Criticality in Quasitopological Gravity
• Isolated critical point from Lovelock gravity
• Critical behavior of charged Gauss-Bonnet AdS black holes in the grand canonical ensemble
• The $D\to 2$ Limit of General Relativity
• Effective scalar-tensor description of regularized Lovelock gravity in four dimensions
• Holographic Black Hole Chemistry
• Einstein gravity with Gauss-Bonnet entropic corrections
• Black holes in the four-dimensional Einstein-Lovelock gravity
• A note on the total action of $4D$ Gauss-Bonnet theory
• Amplitudes and 4D Gauss-Bonnet Theory
• Holographic heat engines: general considerations and rotating black holes
• Thermodynamics of hairy black holes in Lovelock gravity
• Regularized Lovelock gravity
• BTZ black holes with higher curvature corrections in the 3D Einstein-Lovelock theory
• Hairy black holes in cubic quasi-topological gravity
• On the throttling process of the Kerr-Newman-anti-de Sitter black holes in the extended phase space
• Range of novel black hole phase transitions via massive gravity: Triple points and N-fold reentrant phase transitions
• Black hole chemistry and holography in generalized quasi-topological gravity
• On generalized quasi-topological cubic-quartic gravity: thermodynamics and holography
• Criticality for charged black branes
• Hairy Black Hole Chemistry
• Anomalous critical exponents in the anisotropic Ashkin-Teller model
• Charged black hole chemistry with massive gravitons
• Conical Holographic Heat Engines
• Nonsingular black holes and nonsingular universes in the regularized Lovelock gravity
• Nonlinearly Charged Black Hole Chemistry with Massive Gravitons in the Grand Canonical Ensemble
• Holographic Joule-Thomson Expansion in Lower Dimensions
• Holographic Heat Engines Coupled with Logarithmic $U(1)$ Gauge Theory
• Critical Exponents in a Quantum Phase Transition of an Anisotropic 2D Antiferromagnet